Cosmic String Created from Vacuum Fluctuation

The possibility of the cosmic string creation by the vacuum fluctuations of quantum fields in the self-consistent semiclassical theory of gravity is discussed. We use the approximate method for obtaining vacuum expectation value of the renormalized stress-energy tensor of conformally invariant quantum fields in static cylindrically symmetric spacetimes. We have obtained the particular solutions of Einstein equations for the different boundary conditions at the cylinder symmetry axis. There is very interesting question: can the vacuum fluctuation of quantum fields to be the single source of curvature or nontrivial topological structure of spacetime? One may find the solution of this problem in the theory of quantum gravity. But a fully satisfactory theory of quantum gravity does not yet exist. As a first step on the way of solution of this problem one may to use the self-consistent semiclassical theory of gravity. This theory sets the classical Einstein tensor equal to the expectation value of the stress-energy tensor operator of the quantized matter fields present (throughout we use units such that c = h̄ = G = 1)